All terms through 62 (as well as the term 83, which is in the sequence, but might not be next) were confirmed as having a corresponding prime expression of the form x^y + y^x using the online Magma Calculator. The next terms after 62 are probably 80, 83, 84, 87, 94, 129, 135, 136, 140, 142, 146, 149, 152, 158, 175, 185, 194, 199, 205, 206, 207, 221, 222, 227; these are the only values of n in 62 < n <= 236 for which at least one pair (x,y) yields a value of x^y + y^x that is a probable prime. Of these (at least probable) terms, 83 is definitely in the sequence (as 9^422 + 422^9 is definitely prime, and 9+422=431=prime(83)); for the rest, the probablyprime x^y + y^x with the smallest x (there may be more than one) is as follows:
prime(80) = 409: 91^318 + 318^91;
prime(84) = 433: 111^322 + 322^111;
prime(87) = 449: 214^235 + 235^214;
prime(94) = 491: 20^471 + 471^20;
prime(129) = 727: 91^636 + 636^91;
prime(135) = 761: 98^663 + 663^98;
prime(136) = 769: 364^405 + 405^364;
prime(140) = 809: 365^444 + 444^365;
prime(142) = 821: 87^734 + 734^87;
prime(146) = 839: 329^510 + 510^329;
prime(149) = 859: 423^436 + 436^423;
prime(152) = 881: 291^590 + 590^291;
prime(158) = 929: 441^488 + 488^441;
prime(175) = 1039: 325^714 + 714^325;
prime(185) = 1103: 513^590 + 590^513;
prime(194) = 1181: 278^903 + 903^278;
prime(199) = 1217: 61^1156 + 1156^61;
prime(205) = 1259: 101^1158 + 1158^101;
prime(206) = 1277: 394^883 + 883^394;
prime(207) = 1279: 376^903 + 903^376;
prime(221) = 1381: 634^747 + 747^634;
prime(222) = 1399: 384^1015 + 1015^384;
prime(227) = 1433: 397^1036 + 1036^397. (End)
